Multi-dimensional Reduction and Transfer Function Design using Parallel Coordinates

Multi-dimensional transfer functions are widely used to provide appropriate data classification for direct volume rendering. Nevertheless, the design of a multi-dimensional transfer function is a complicated task. In this paper, we propose to use parallel coordinates, a powerful tool to visualize high-dimensional geometry and analyze multivariate data, for multi-dimensional transfer function design. This approach has two major advantages: (1) Combining the information of spatial space (voxel position) and parameter space; (2) Selecting appropriate high-dimensional parameters to obtain sophisticated data classification. Although parallel coordinates offers simple interface for the user to design the high-dimensional transfer function, some extra work such as sorting the coordinates is inevitable. Therefore, we use a local linear embedding technique for dimension reduction to reduce the burdensome calculations in the high dimensional parameter space and to represent the transfer function concisely. With the aid of parallel coordinates, we propose some novel high-dimensional transfer function widgets for better visualization results. We demonstrate the capability of our parallel coordinates based transfer function (PCbTF) design method for direct volume rendering using CT and MRI datasets.